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A decision-theoretic approach to dealing with uncertainty in quantum mechanics

Created by
  • Haebom

Author

Keano De Vos, Gert de Cooman, Alexander Erreygers, Jasper De Bock

Outline

This paper presents a decision-theoretic framework for dealing with quantum mechanical uncertainty. This uncertainty has two aspects: first, there is uncertainty about the state of a quantum system, and second, there is the inherent aspect of quantum mechanical uncertainty: even if the quantum state is known, the outcome of a measurement can remain uncertain. In this framework, measurements serve as actions with uncertain outcomes, and simple decision-theoretic assumptions ensure that Born's rule is included in the utility function associated with these actions. This approach separates (exact) probability theory from quantum mechanics, leaving room for a more general, so-called uncertain probability approach. This paper discusses the mathematical implications and provides a decision-theoretic foundation for the recent seminal work of Benavoli, Facchini, and Zaffalon, comparing it with an earlier approach by Deutsch and Wallace.

Takeaways, Limitations

Takeaways: Provides a new decision-theoretic framework for quantum mechanical uncertainty, suggesting the possibility of incorporating Born's rule into utility functions and separating probability theory from quantum mechanics. It provides a decision-theoretic foundation for the work of Benavoli, Facchini, and Zaffalon. It also opens the door to considering uncertain probability approaches.
Limitations: There is insufficient discussion on the practical applicability and experimental validation of the proposed framework. A more in-depth comparison with the approach of Deutsch and Wallace is needed. A detailed explanation of the specific application of the uncertain probability approach is needed.
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